Question 81569
You are given two equations and two unknowns. Anytime you have at least as many equations as you have unknowns, you can solve the problem!
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Let the two numbers in question be called x and y.
From the given information we can say:
Equation #1: {{{x+y=35}}}
and
Equation #2: {{{x-y=13}}}
So, you have 2 equations and 2 unknowns. you are good to go.
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First, Solve Equation #2 for x in terms of y:
{{{x=13+y}}}
Now, substitute this expression for x into Equation #1 (that is why this is called the "substitution" method.
{{{13+y+y=35}}}
Solve for y:
{{{2y=22}}}
{{{highlight(y=11)}}}
Now, substitute this value for y back in to Equation #2:
{{{x-11=13}}}
Solve for x:
{{{highlight(x=24)}}}
Check these answers by plugging the values back in to the original equations. They should both hold true.
Good Luck,
tutor_paul@yahoo.com